Question

A tetromino consists of four squares connected along their edges. There are five possible tetromino shapes, $\mathrm{I}$ , $\mathrm{O}$ , $\mathrm{L}$ , $\mathrm{T}$ , and $\mathrm{S}$ , shown below, which can be rotated or flipped over. Three tetrominoes are used to completely cover a $3 \times 4$ rectangle. At least one of the tiles is an $\mathrm{S}$ tile. What are the other two tiles?

$\mathrm{I}$ and $\mathrm{L}$

$\mathrm{I}$ and $\mathrm{T}$

$\mathrm{L}$ and $\mathrm{L}$

$\mathrm{L}$ and $\mathrm{S}$

$\mathrm{O}$ and $\mathrm{T}$

Answer: C

Concepts:tiling casework

Difficulty rating: 1140

Small Hint:

Try placing the $\mathrm{S}$ tile so the leftover region separates cleanly

Big Hint:

After one $\mathrm{S}$ tile is placed, check which pair can tile the rest

Video solution:

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Written solution:

A little trial-and-error suggests placing the $\mathrm{S}$ tetromino in a way that does not block too much, like this:

It is then easy to see that the remainder can be partitioned into two $\mathrm{L}$ tetrominoes, and so the answer is C.

2025 AMC 8 Problem 11